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Special functions in gnuplot

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Can someone give me some pointers on how can I figure out:

a) what ALGORITHMS (files/codes either gnuplot specific or system specific) gnuplot is ACCESSING to calculate special functions like gamma, or lgamma, igamma, ibeta etc..... and WHERE are these algorithms/files located

and,

b) (if possible) tell me (or guide me on how to find) how accurate are these estimates and over what range of values for their arguments.

I am using these functions in the "fit" command and not merely for plotting. Hence it is extremely important for me to know the error bounds of these estimates and the range of values over which they are valid. 


Any help will be much appreciated. [Please read the background below before responding].

I am using: Scientific Linux 6.2 (Kernel Linux 2.6.32-220.23.1.el6.x86_64)


BACKGROUND:
=============
I hunted for this information a bit and have come across a file called specfun.c in the gnuplot /src directory. The file contains lines of code with:

ifdef ..., ifndef... and ifdef HAVE_function

I think that something like HAVE_LGAMMA indicates that if a function called LGAMMA exists then that one is preferred. 

BUT, WHERE is GNUPLOT looking for such pre-existing LGAMMA (and other function definitions)? 

[I dont understand what "HAVE_function" type references really mean. I searched a lot but could not really understand what it is doing and WHERE exactly is it looking so that I can go to that file and take a look at the algorithm used to define that function].

Also is LGAMMA the same as "log gamma" or is it "gamma in long format/type (i.e. double precision)". If it is "log gamma" then why is a call to gamma(x) referred to lgamma(x) without any 'exponentiation'? 

This link indicates that lgamma is log(gamma) and not just gamma in double-precision.

http://www.kernel.org/doc/man-pages/online/pages/man3/lgamma.3.html

But I am not sure if gnuplot is accessing this one or not. I also do not know WHERE to find this lgamma in my system files.

I also checked the GNU scientific library, but here gamma is referred to differently and not as lgamma:
http://www.gnu.org/software/gsl/manual/html_node/Gamma-Functions.html

Further, the GNU scientific library also has igamma defined:
http://www.gnu.org/software/gsl/manual/html_node/Incomplete-Gamma-Functions.html

BUT, the GNUPLOT specfun.c file does not seem to use this function even if it exists in the GNU scientific library. Anyone knows why? Is the gnuplot version of igamma more accurate than that in the GNU scientific library?

Please give me as specific info as possible (given my operating system..see above). Like if you say system file, then let me know whether you are referring to:

usr/lib/x86_64-redhat..... 

OR

usr/include/ etc..

And once again, I dont just want to know what it is doing, I want to know (and see for myself) what ALGORITHM it is accessing and if possible get some idea of what are the errors in estimation of these special functions and over what range of values for its arguments.

Thank you very much for your help in advance!
Kind regards,
Barun.

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Special functions in gnuplot boruun@gmail.com - 2012-08-10 20:34 -0700
  Re: Special functions in gnuplot sfeam <sfeam@users.sourceforge.net> - 2012-08-10 23:05 -0700
  Re: Special functions in gnuplot boruun@gmail.com - 2012-08-14 12:39 -0700
  Re: Special functions in gnuplot boruun@gmail.com - 2012-08-14 12:37 -0700
    Re: Special functions in gnuplot Dr Engelbert Buxbaum <engelbert_buxbaum@hotmail.com> - 2012-09-11 11:26 -0400
  Re: Special functions in gnuplot hogney@gmail.com - 2012-08-18 08:34 -0700
    Re: Special functions in gnuplot sfeam <sfeam@users.sourceforge.net> - 2012-08-18 10:56 -0700

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